Genomic analysis of the slope of the reaction norm for body weight in Australian sheep

Table 1 Variance of the additive genetic intercept (\({{\varvec{\sigma}}}_{{\varvec{a}}\mathbf{1}\boldsymbol{ }}^\mathbf{2}\)) and slope (\({{\varvec{\sigma}}}_{{\varvec{a}}\mathbf{2}\boldsymbol{ }}^\mathbf{2}\)), the residual intercept (\({{\varvec{\sigma}}}_{{\varvec{e}}\mathbf{1}\boldsymbol{ }}^\mathbf{2}\)), slope (\({{\varvec{\sigma}}}_{{\varvec{e}}\mathbf{2}\boldsymbol{ }}^\mathbf{2}\)) and covariance (\({{\varvec{\sigma}}}_{{\varvec{e}}\mathbf{1}\boldsymbol{ }}{{\varvec{\sigma}}}_{{\varvec{e}}\mathbf{2}}\)), as well as genetic group (g) variance

Model^a	\({{\varvec{\sigma}}}_{{\varvec{a}}\mathbf{1}\boldsymbol{ }}^\mathbf{2}\)	\({{\varvec{\sigma}}}_{{\varvec{a}}\mathbf{2}\boldsymbol{ }}^\mathbf{2}\)	\({{\varvec{r}}}_{{\varvec{a}}\mathbf{1}{\varvec{a}}\mathbf{2}}\)	\({{\varvec{\sigma}}}_{{\varvec{e}}\mathbf{1}\boldsymbol{ }}^\mathbf{2}\)	\({{\varvec{\sigma}}}_{{\varvec{e}}\mathbf{2}\boldsymbol{ }}^\mathbf{2}\)	\({{\varvec{\sigma}}}_{{\varvec{e}}\mathbf{1}{\varvec{e}}\mathbf{2}}\)	g	LKH
RNM-HOM	7.40 (0.31)	1.28 (0.16)	0.52 (0.04)	17.52 (0.26)	–	–	11.45 (3.85)	− 46,938.28
RNM-HET	6.98 (0.31)	1.19 (0.17)	0.18 (0.06)	18.17 (0.31)	− 0.32 (0.23)	1.55 (0.14)	10.88 (3.69)	− 46,870.32^b

The correlation between additive genetic intercept and slope (\({r}_{{\varvec{a}}\mathbf{1}{\varvec{a}}\mathbf{2}}\)) and the log-likelihood (LKH) are also reported
^aRNM-HOM: linear reaction norm model with homogenous residual variance; RNM-HET: linear reaction norm model with heterogenous residual variance
^bBased on a log-likelihood ratio test using a chi-square distribution, RNM-HET provided a better fit (p = 1.7 × 10¹⁵)

ISSN: 1297-9686